Custom Made Solid of Revolution

In the applet below, you'll see an image of a vase. 14 points are plotted along the surface of this vase. You can move these points anywhere you'd like at any time! The function drawn below is the function-of-best-fit. You can adjust the degree of this polynomial function by using the degree slider. Can you position the white points and find the best degree of the polynomial of best fit so that the surface of revolution GeoGebra creates looks most like the vase seen to the left?

Quick (Silent) Demo